Simulated annealing study of gyroid formation in diblock copolymer solutions

Conditions for the formation of gyroid structures in diblock copolymer solutions are examined using a simulated annealing technique. The simulations were performed on diblock copolymer systems of A(N_A)-b-B(N_B) (with N_A<N_B) in solvents that are selective to the A blocks. It is shown that gyroid structures form in a narrow range of block copolymer concentrations between the hexagonally packed cylindrical and the lamellar phases and at an almost constant B-monomer concentration. It is also shown that the gyroid structure is especially sensitive to the B-solvent interaction (ε_BS) and the length of the B block (N_B). Phase diagrams for the diblock copolymer solutions are constructed. These predicted results are consistent with previous experimental observations. The three-dimensional isosurface contour plots of the simulated gyroid structure shows two interpenetrating strut networks. The projection along the [111] direction of the simulated gyroid structure and the spherically averaged structure factor are in good agreement with previous experimental results.